The following correction was printed in the Guardian's Corrections and clarifications column, Friday 21 May 2010

Maxine Peake was described as having a Yorkshire accent. She was born and brought up in Bolton, which is historically a part of Lancashire, now Greater Manchester, the main of eight townships within Bolton metropolitan borough.

Maxine Peake does not arrive for our interview alone. That is not unusual – actors often come trailing clouds of PR wonks, and photographers, and stylists and maybe a girl Friday to hold the hairdryer for those windswept shots.

But Peake's retinue is far more endearing: she brings her dad. Brian Peake is a retired lorry driver from Bolton. He has been in London for the night to accompany Maxine to the opening gala of the London Lesbian & Gay Film Festival. The festival was launched with a showing of The Secret Diaries Of Miss Anne Lister, a new BBC2 period drama about the illicit passions of a lesbian Victorian landowner. And Peake, of course, has the star part as the haughty, irrepressible Anne Lister, who strides across the Yorkshire moors in a rakish black top hat, auburn tresses blowing in the wind.

I'm not sure I'd have brought my dad to a lesbian erotic costume drama, complete with bedroom scenes, but Mr Peake tells me he loved it and the party afterwards was great. But the best thing of all, he says, with an amazed and satisfied sigh, was seeing the words "Maxine Peake" emblazoned across the screen. Then, newspaper and coffee in hand, he disappears and I'm left with Maxine.

The difference between the real Peake and the screen Peake is a bit of a shock. As Lister she was a huge, uncompromising personality. In Shameless she played the loud, brassy neighbour Veronica. So, being such a big screen presence, by rights she should also be a rather imposing person in the flesh. But instead she's petite and smiley, with shiny blue eyes and a small, straight nose. It's a delicate face, slightly feline even. She is chatty and friendly and speaks fast, with a broad Yorkshire accent. She tells me the premiere was "lively".

And the party afterwards? Did she make a late night of it?

"Only midnight. At about 11 o'clock I was saying to my dad, 'Any chance we could go?' I was a little bit concerned. Will he be all right? But he was having a whale of a time, so I was sat there waiting for him to finish up." And that is when she laughs. It's not a delicate titter, but a 12-pint-a-night-out-on-the–tiles-Ginsters-meat-and-gravy sort of snort.

When she's recovered – and the china doll eyes and the porcelain features are back in place – she says rather sweetly, "Yeah, I know. People say I have such a dirty laugh."

I ask about the sex scenes.

"Yeah, that was weirdly fine."

She's not gay?

"No, I'm not," she says a little pensively.

A partner?

"No." She grins. "It's a bit of a sore subject."

Those seemingly difficult things for actors – nude scenes, or shots where you humiliate yourself, where you weep and, as she says, "the snot goes everywhere" don't seem to present Peake with problems. It's watching it afterwards she can't bear. "I know a lot of actors who say, 'I don't watch myself.' And I went through a phase of not watching myself because it is painful. But I feel I have still got so much to learn."

Why painful?

"Unfortunately," she says, "at the end of the day, when you watch yourself on the screen you are always you."

She has hit on an eternal truth. Actors always will be disappointed when they see their own performance. It's not just a question of camera angles and being crazily vain (as many are – though she isn't). But part of the chemistry of acting has to be a suspension of disbelief – by everyone. Good actors must, if even for a slither of a second, believe in their own transfiguration.

And it has to be said that Maxine Peake is one of our very good actors. She is not a household name. Nor is she a terribly familiar face. She is a rising star – but a rather old one. For Peake is 35. The camera loves her, but she has missed out on being a Beautiful Young Thing.

The reason is simple. Peake doesn't come from a thespian background: her family are solidly working class. She may have learned her socialist politics on the knee of her grandfather, Jim, to whom she is still very close, but this wasn't an environment that nurtured acting talent. At school, like so many budding actors, Peake played the class show-off and clown. And she tells the story of climbing on top of a cupboard in a German class just to surprise the teacher ("At 13 I thought that was hilarious"). She would, she says, do anything then for effect and she was dying to become an actor. "But I didn't really know how you went about it. There were nobody's parents, nobody's relatives, who were actors. It was three years before I got to drama school. I went to Salford tech. They did a two-year performing arts course. I went there singing and dancing – I had a terrible time. I turned up in green dungarees and German power boots. I was into prog rock at the time – Gong and Hawkwind – and I was clumping around. There was about six or seven of us who were misfits… and by the end there was only me left. Everybody else was edged out. Me, being stubborn, I saw the course through."

But the spark must already have been burning bright, because Peake was accepted by Rada. She couldn't afford to go and the South Bank Show made a film following her fortunes as she searched for sponsorship. Rada, meanwhile, put her forward for the Patricia Rothermere scholarship. Peake recounts how, at the audition, she met a lovely girl from Wales. Afterwards, assuming the lovely girl from Wales had won the bursary, Peake never bothered to phone back to get the results.

But she had won. And she tells me that when she phoned home with the good news, her mother couldn't stop crying. And as Peake recounts this – her mother died only 18 months ago – she, too, starts to cry. I slide my wine glass across the table. She takes a drink, dabs her eyes on the napkin, gives a little shiver, laughs, apologises and then – quick as that – we are back on track again.

At Rada, Peake's troubles weren't over. The staff, she says, criticised her acting as overly naturalistic and they didn't like her accent. Also, she was a big girl then and fond of her food. "One teacher said to me, 'Maxine, if you don't lay off the chips, you'll never play Juliet.' And I went [she does a sulky, braying voice], 'I don't wanna play Juliet.' But of course I did."

After Rada, Peake got a part in Victoria Wood's sitcom Dinnerladies where she played the young, taciturn Twinkle. The part, she says, "was a gift. I didn't have much to say – you don't need much." But watching the early episodes, Twinkle doesn't look like a hot new hope for the future – she is just a great, big monosyllabic podge in a silly catering hat. Indeed, her performance was so deadpan and flat that there were some doubts whether she was acting at all. "The first couple of castings after Dinnerladies, people thought I'd just drifted in off the street and they'd go, 'So where did Victoria find you?' And I'd say, 'Well, I've just left Rada.' And they went, 'You what!' ''

Advised by Wood, she began to diet. She lost five stone (32kg) and becoming thin has transformed her appearance – the outlines of her face have become more defined and, somehow, more in focus. Now she looks less like a mortal and more of an actor – fine, fragile, sensitive. But, of course, the old Maxine lives on underneath and the big, loud northern lass is always lying in wait ready to spring out and bellow with laughter. This does give her performances a certain edge. There are few actors who can so surprise you with changes of tempo and gusts of anger and sudden explosions of mirth.

The teachers at Rada had advised her to lose her accent, but Peake thinks that, on the contrary, it has probably helped her career. "To be honest," she says, "we are all as talented as each other. It's whether you fit. Sometimes it boils down to having the right hair." And she has been in several northern films including Red Riding and See No Evil: The Moors Murders where she plays a nervy, very believable Myra Hindley. There was also the decidedly gruesome Messiah, where she played a detective under intense pressure. In one scene in the investigation room, as the murders begin to mount up, Peake's character presents a calm front, but when she holds up a photograph you can see her hand is ever so slightly shaky. I remark on this tiny, telling detail.

"Look," says Peake. And she holds up her hand. It quivers. "I am a shaker. I always have been. But you can use it."

She is also a cryer. In the BBC1 drama Criminal Justice she plays Juliet, a nervous middle-class wife accused of murder. And there is one particularly memorable moment: she's standing in the dock and when the judge refuses her bail, Juliet's face remains completely still. All you see is a tear bolt down her cheek. The scene is extraordinarily moving. But Peake doesn't take compliments easily. "Ahh!" she squirms. "Crying does not equal good acting. Sometimes you are just crying because you don't know what you are doing. Stop it! Pack it in!

"I know I sometimes come across as being quite dismissive about acting. But I'm not. It's like people reading their diaries in public. I don't want to talk about how I create characters. I find it self-indulgent." Then she adds: "And I hate that word – 'method' – actor. So many people say, 'I'm a method actor.' No, you're not! You're just a pain in the arse!''

Pain in the arse or not, Peake herself is deadly serious about her own artistic integrity and most exacting about her work. She won't, she says, take on a role unless it feels impossibly difficult and quite different from what she's done before. She also has to be ready. At the moment she's not doing anything. But soon, she feels, the time will be right again. She says solemnly, "I would love to do more female-driven dramas and I would love to do something about suffragettes and the women's movement."

And what about something a little less earnest? Perhaps a Hollywood action movie?

A huge, beguiling smile spreads across her face. "I'd love to do a big kick-arse movie. Train up and be some hard, ballsy Blonde Fist 2. Yeah! A remake is in order."